Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

TL;DR

This paper reviews the statistical methods for detecting deterministic gravitational-wave signals in stationary Gaussian noise, introducing tools and algorithms for optimal data analysis and parameter estimation.

Contribution

It provides a comprehensive theoretical framework and practical algorithms for gravitational-wave signal detection in Gaussian noise, including formulas for various signal types.

Findings

Introduction of optimal signal-to-noise ratio and Fisher matrix tools

Formulas for general gravitational-wave signals in Gaussian noise

Discussion of efficient algorithms for data analysis

Abstract

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, $\mathcal{F}$-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.